Day One Proportions Homework Day 1 of 3 15 Min Target
Scale Proportions Daily Homework
Constant of Proportionality (Tables), Scaled Figures & Equation Fluency
Name:
Date: Per:
Part 1: Fluency Warm-Up • One-Step Equations
Show inverse operations in the work box.
\(x + 18 = 45\)
\(x =\)
\(y - 14 = 37\)
\(y =\)
\(6x = 78\)
\(x =\)
\(\frac{y}{7} = 9\)
\(y =\)
Part 2: Constant of Proportionality • \(k = \frac{y}{x}\)
Equation form: \(y = kx\)
5. Car Wash Fundraiser Earnings
Calculate ratio \(\frac{y}{x}\) for each row. Then state \(k\) and the equation.
Cars (\(x\)) Money (\(y\)) Ratio \(\frac{y}{x}\) Work 3 $36 5 $60 8 $96
Constant (\(k\)): \(k =\) _______
Equation (\(y = kx\)): \(y =\) _______
6. Bakery Flour Recipe
A baker uses 15 cups of flour to bake 6 identical loaves of bread. Loaves (\(x\)) and cups of flour (\(y\)) are proportional.
a. Calculate constant of proportionality (\(k\)):
\(k =\) ____________ cups/loaf
b. Write the equation relating \(x\) and \(y\):
\(y =\) ______________________
Meaning: Each loaf requires cups of flour.
Part 3: Scaled Figures • Original vs. New & Scale Factor
Compare corresponding side lengths to find the scale factor.
7. Identifying Original vs. New Image & Calculating Scale Factor
Marcus has a printed photograph that measures 4 inches by 6 inches. He creates a large wall poster that measures 20 inches by 30 inches.
Original Image:
New Scaled Image:
Scale Factor:
8. Classify each pair as an Enlargement, Reduction, or Congruent figure based on side lengths.
Pair Original Side New Scaled Side Comparison Classification A. Rectangle base 16 cm 4 cm New < Original B. Triangle height 5 in 15 in New > Original C. Blueprint room 12 ft 12 ft New = Original
Unit 2: Ratios, Proportions & Scale Factors Self-Check: Did you solve for both \(x\) and \(y\) in Part 1?
Day One Proportions Answer Key Answer Key Day 1 of 3 • Quick Grade
Scale Proportions Daily Homework
Teacher Reference • Solutions, Work & Grading Guidance
Points Total: 10 Points
• Part 1: 4 pts (1 pt each)
Part 1: Fluency Solutions • One-Step Equations
1 point each (correct step & answer)
\(x + 18 = 45\)
\(x = 45 - 18\)
\(x = 27\)
\(x = 27\)
\(y - 14 = 37\)
\(y = 37 + 14\)
\(y = 51\)
\(y = 51\)
\(6x = 78\)
\(x = \frac{78}{6}\)
\(x = 13\)
\(x = 13\)
\(\frac{y}{7} = 9\)
\(y = 7 \cdot 9\)
\(y = 63\)
\(y = 63\)
Part 2: Constant of Proportionality Solutions
Verify \(k = \frac{y}{x}\) is constant across all entries
5. Car Wash Fundraiser Earnings
Proportional because all \(\frac{y}{x}\) ratios simplify to 12.
Cars (\(x\)) Money (\(y\)) Ratio \(\frac{y}{x}\) 3 $36 \(\frac{36}{3} = 12\) 5 $60 \(\frac{60}{5} = 12\) 8 $96 \(\frac{96}{8} = 12\)
Constant (\(k\)): \(k = 12\)
Equation: \(y = 12x\)
6. Bakery Flour Recipe
\(x = 6\) loaves, \(y = 15\) cups flour.
a. Constant of proportionality (\(k\)):
\(k = \frac{15}{6} = \frac{5}{2} = 2.5\) \(k = 2.5\) cups/loaf
b. Equation:
\(y = 2.5x\) Â (or \(y = \frac{5}{2}x\))
Meaning: Each loaf of bread requires 2.5 cups of flour.
Part 3: Scaled Figures Solutions
Side length comparisons & scale factor
7. Identifying Original vs. New Image & Scale Factor
Original photograph \((4 \times 6) \rightarrow\) New wall poster \((20 \times 30)\).
Original Image:
Photo (4 in × 6 in)
New Scaled Image:
Poster (20 in × 30 in)
Scale Factor:
\(\frac{\text{New}}{\text{Orig}} = \frac{20}{4} = 5\)
8. Classification based on side lengths:
Day Two Proportions Homework Day 2 of 3 15 Min Target
Scale Proportions Daily Homework
Constant of Proportionality (Graphs & Equations), Scale Factors & Equation Fluency
Name:
Date: Per:
Part 1: Fluency Warm-Up • One-Step Equations
Show inverse operations in the work box.
\(y + 27 = 64\)
\(y =\)
\(x - 35 = 48\)
\(x =\)
\(8y = 72\)
\(y =\)
\(\frac{x}{9} = 7\)
\(x =\)
Part 2: Proportionality in Graphs & Equations
Graph point \((1, k)\) identifies the unit rate.
5. Biking Distance Graph
A line passes through \((0, 0)\), \((2, 28)\), and \((4, 56)\), where \(x\) is hours and \(y\) is miles.
a. Ratio \(\frac{y}{x}\) using point \((2, 28)\): \(k =\)
b. Coordinates of unit rate point: \((1,\) \()\)
c. Equation representing line: \(y =\)
Explain meaning: The cyclist travels miles in 1 hour.
6. Equation Identification
Proportional equations must follow \(y = kx\) (passes through origin \((0,0)\)).
Equation Proportional? Constant (\(k\)) A. \(y = 7.5x\) YES Â /Â NO \(k =\) _____ B. \(y = 4x + 9\) YES Â /Â NO _____ C. \(y = \frac{3}{5}x\) YES Â /Â NO \(k =\) _____
If not proportional, why not?
Part 3: Scale Factor • \(\text{Scale Factor} = \frac{\text{New}}{\text{Original}}\)
Classification based on Scale Factor value
7. Calculating Scale Factor from Dimensions
Calculate the scale factor as a simplified fraction or whole number using \(\frac{\text{New}}{\text{Original}}\).
Scenario A: Graphic Design Logo
Original = 8 cm → New = 32 cm
Work: \(\frac{\text{New}}{\text{Orig}} =\) Scale Factor =
Scenario B: Model Airplane
Original = 50 ft → New = 10 ft
Work: \(\frac{\text{New}}{\text{Orig}} =\) Scale Factor =
8. Classify each scale factor as an Enlargement (\(k > 1\)), Reduction (\(k < 1\)), or Congruent (\(k = 1\)).
Scale Factor (\(k\)) Value vs. 1
Day Two Proportions Answer Key Answer Key Day 2 of 3 • Quick Grade
Scale Proportions Daily Homework
Teacher Reference • Solutions, Work & Grading Guidance
Points Total: 10 Points
• Part 1: 4 pts (1 pt each)
Part 1: Fluency Solutions • One-Step Equations
1 point each (correct step & answer)
\(y + 27 = 64\)
\(y + 27 - 27 = 64 - 27\)
\(y = 37\)
\(y = 37\)
\(x - 35 = 48\)
\(x - 35 + 35 = 48 + 35\)
\(x = 83\)
\(x = 83\)
\(8y = 72\)
\(\frac{8y}{8} = \frac{72}{8}\)
\(y = 9\)
\(y = 9\)
\(\frac{x}{9} = 7\)
\(9 \cdot \frac{x}{9} = 9 \cdot 7\)
\(x = 63\)
\(x = 63\)
Part 2: Proportionality in Graphs & Equations Solutions
Slope / Unit rate through origin
5. Biking Distance Graph
Line passes through \((0, 0)\), \((2, 28)\), and \((4, 56)\).
a. Ratio \(\frac{y}{x} = \frac{28}{2}\): \(k = 14\)
b. Unit rate point: \((1, 14)\)
c. Equation: \(y = 14x\)
Meaning: The cyclist travels 14 miles every 1 hour (speed of 14 mph).
6. Equation Identification Solutions
Must fit \(y = kx\) (must pass through the origin \((0,0)\)).
Equation Proportional? Constant (\(k\)) A. \(y = 7.5x\) YES \(k = 7.5\) B. \(y = 4x + 9\) NO None (N/A) C. \(y = \frac{3}{5}x\) YES \(k = \frac{3}{5}\) (or \(0.6\))
If not proportional, why not? Equation B has a \(y\)-intercept of \(+9\); when \(x = 0\), \(y = 9\) (does not pass through origin).
Part 3: Scale Factor Solutions
\(\text{Scale Factor} = \frac{\text{New}}{\text{Original}}\)
7. Calculating Scale Factor from Dimensions
Always write ratio as \(\frac{\text{New}}{\text{Original}}\) and simplify.
Scenario A: Graphic Design Logo
Orig = 8 cm → New = 32 cm
\(\frac{32}{8} = 4\) Scale Factor = 4
Scenario B: Model Airplane
Orig = 50 ft → New = 10 ft
Day Three Proportions Homework Day 3 of 3 15 Min Target
Scale Proportions Daily Homework
Synthesis: Proportions, Missing Dimensions & Scaling Mastery
Name:
Date: Per:
Part 1: Fluency Warm-Up • One-Step Equations
Show inverse operations in the work box.
\(12x = 96\)
\(x =\)
\(\frac{y}{4} = 18\)
\(y =\)
\(x - 47 = 35\)
\(x =\)
\(y + 29 = 84\)
\(y =\)
Part 2: Constant of Proportionality • Context & Prediction
Apply \(k = \frac{y}{x}\) and \(y = kx\)
5. Solar Panel Energy Generation
A rooftop solar array produces 45 kilowatt-hours (kWh) of electricity in 6 hours of direct sunlight. The hours of sun (\(x\)) and electricity produced (\(y\)) are proportional.
a. Find Constant (\(k\))
Ratio \(\frac{y}{x}\) with units:
\(k =\) kWh/hr
b. Equation & Point
Equation & unit rate point:
\(y =\)
\((1,\) \()\)
c. Prediction
How many kWh in 10 hours?
\(y =\) kWh
Part 3: Scale Factor Applications • Missing Dimensions
\(\text{New Dimension} = \text{Original Dimension} \times \text{Scale Factor}\)
6. Finding New Scaled Dimensions
An artist's sketch has length 5 cm and width 3 cm. She uses a scale factor of 4.5 for her canvas.
New Length: cm
New Width: cm
Classification:
7. Calculating Scale Factor from Side Lengths
A rectangular gym court is 80 feet long. On a coach's diagram sheet, the court is drawn as 10 inches long.
Original image:
New scaled image:
Classification:
Scale ratio: 1 in represents feet.
8. Comprehensive Scale Factor & Image Classification Check
State whether each represents an Enlargement, Reduction, or Congruent figure:
a. Scale Factor \(k = \frac{7}{8}\)
b. Scale Factor \(k = 1.0\)
c. Side: 12 cm → 36 cm
Unit 2: Ratios, Proportions & Scale Factors • Series Complete Check all work: Have you completed all 8 questions?
Day Three Proportions Answer Key Answer Key Day 3 of 3 • Quick Grade
Scale Proportions Daily Homework
Teacher Reference • Solutions, Work & Grading Guidance
Points Total: 10 Points
• Part 1: 4 pts (1 pt each)
Part 1: Fluency Solutions • One-Step Equations
1 point each (correct step & answer)
\(12x = 96\)
\(x = \frac{96}{12}\)
\(x = 8\)
\(x = 8\)
\(\frac{y}{4} = 18\)
\(y = 4 \cdot 18\)
\(y = 72\)
\(y = 72\)
\(x - 47 = 35\)
\(x = 35 + 47\)
\(x = 82\)
\(x = 82\)
\(y + 29 = 84\)
\(y = 84 - 29\)
\(y = 55\)
\(y = 55\)
Part 2: Constant of Proportionality Solutions
\(k = \frac{y}{x}\) and \(y = kx\)
5. Solar Panel Energy Generation
\(x = 6\) hours, \(y = 45\) kWh.
a. Find Constant (\(k\))
\(k = \frac{45}{6} = 7.5\)
\(k = 7.5\) kWh/hr
b. Equation & Point
Unit rate point \((1, k)\):
\(y = 7.5x\)
Point: \((1, 7.5)\)
c. Prediction for 10 Hours
\(y = 7.5(10) = 75\)
\(y = 75\) kWh
Part 3: Scale Factor Mastery Solutions
Dimension calculations & classifications
6. Finding New Scaled Dimensions
Original: 5 cm × 3 cm. Scale Factor = 4.5.
New Length: \(5 \times 4.5 = 22.5\text{ cm}\)
New Width: \(3 \times 4.5 = 13.5\text{ cm}\)
Classification: Enlargement (since \(4.5 > 1\))
7. Identifying Original vs. New Image
Gym court = 80 ft; Coach's diagram = 10 inches.
Original image: Actual Gym Court
New scaled image: Coach's Diagram
Classification: Reduction
Scale ratio: 1 in represents 8 feet (\(80 \div 10 = 8\)).
8. Comprehensive Scale Factor & Image Classification Check
Full classification summary:
a. Scale Factor \(k = \frac{7}{8}\)
Since \(k < 1\):
Reduction
b. Scale Factor \(k = 1.0\)
Since \(k = 1\):
Congruent
c. Side: 12 cm → 36 cm
Since New > Orig:
